452 INDEX
Self-adjoint unbounded operator: 15.12
Seminorm: 12.14
Separation (of two sets by a hyperplane):
12.15, prob. 4
Series in a topological vector space: 12.14
Simple convergence, limit: 12.5
Simple normal operator: 15.11
Simplex: 14.3
Spectral radius: 15.2
Spectral value of an element of a normed
algebra: 15.2
Spectrum of an element of a Banach algebra:
15.2
Spectrum of a Banach algebra: 15.3
Spectrum of an unbounded operator: 15.12
Square-mtegrable function: 13.11
Stabilizer of a point: 12.10
Stable subspace (for a representation): 15.5
Star algebra: 15.4
Steiner symmetrization: 14.3, prob. 8
Stem's theorem: 14.10, prob. 4
Step function: 13.9
Stieltjes measure: 13.8, prob. 6
Stieltjes' moment problem: 13.20, prob. 5
Stieltjes transform: 14.11, prob. 16
Strict morphism: 12.12
Strong topology: 12.15
Subspace: 12.2
Sum of a series with positive terms: 13.5
Support of a function: 12.6
Support of a measure: 13.19
Symmetric neighborhood: 12.8
Szego-Kolmogoroff-Krein theorem: 15.3,
prob.11
Tessellation (G-): 14.1, prob. 6
Thue's theorem: 14.2, prob. 2
Titchmarsh-Kodaira formula: 15.12, prob.
9
Topological group: 12.8
Topological isomorphism of normed (or
normable) algebras: 15.1
Topological space: 12.1
Topological zero-divisor: 15.2, prob. 3
Topologically cyclic representation: 15.5
Topologically equivalent families of pseudo-
distances: 12.4
Topologically irreducible representation:
15.5
Topologically nilpotent: 15.2, prob. 5
Topologically simple: 15.8
Topology: 12.1
Topology defined by a distance: 12.1
Topology defined by a family of pseudo-
distances: 12.4
Topology defined by a family of seminorms:
12.14
Topology of convergence in measure: 13.12,
prob. 2
Topology of simple convergence: 12.15
Torus: 14.2
Total mass of a bounded measure: 13.9
Totalizer: 15.5
Trace of an operator: 15.11, prob. 7
Transitively (group acting): 12.10
Translation of a function or measure: 14.1
Transpose of a continuous linear mapping:
12.15
Trivial action: 12.10
Type (p,q) (operator): 13.17, prob. 7
U
Unbounded operator: 15.12
Uniformizable space: 12.4
Unimodular group; 14.3
Unitary element: 15.4
Unitary group: 12.15, prob. 8
Universally measurable: 13.9
Upper envelope of a family of real-valued
functions: 12.7
Upper integral: 13.5
Upper semicontinuous function: 12.7
Vague topology: 13.4
Vaguely bounded, convergent, continuous:
13.4
von Neumann's ergodic theorem: 12.15,
prob.12
von Neumann's theorem on unbounded
normal operators: 15.12entiable: